Express this quotient in scientific notation: ${\frac{4.500\times 10^{-1}} {6.0\times 10^{-3}}}$
Explanation: Start by collecting like terms together. $= {\frac{4.500} {6.0}} \times{\frac{10^{-1}} {10^{-3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.75 \times 10^{-1\,-\,-3}$ $= 0.75 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.75$ is the same as $7.50 \div 10$ , or $7.50 \times 10^{-1}$ $ = {7.50 \times 10^{-1}} \times 10^{2} $ $= 7.50\times 10^{1}$